# INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS

@article{Terpereau2013INVARIANTHS,
title={INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS},
author={Ronan Terpereau},
journal={Transformation Groups},
year={2013},
volume={19},
pages={247-281}
}
Let W be a finite-dimensional representation of a reductive algebraic group G. The invariant Hilbert scheme $$\mathcal{H}$$ is a moduli space that classifies the G-stable closed subschemes Z of W such that the affine algebra k[Z] is the direct sum of simple G-modules with prescribed multiplicities. In this article, we consider the case where G is a classical group acting on a classical representation W and k[Z] is isomorphic to the regular representation of G as a G-module. We obtain families… CONTINUE READING

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